Apparatus, e.g. a spectrum analyser or frequency counter, for determining the frequency and/or amplitude of a spectral line in the frequency spectrum of an input signal, comprising a window-defining filter for shaping and truncating the input signal amplitude as a function of time, means for applying a discrete Fourier transform to the filtered input signal to store representations of signal amplitude at each of several predetermined, contiguous frequency bins, and means for interpolating between the stored values of signal amplitude to determine the frequency and/or amplitude of an amplitude peak in the input signal, wherein the interpolation means fits the stored values to a Gaussian or near-Gaussian curve which is close to the Fourier transform of the window function defined by the filter.